The common ratio of a geometric series is $3$ and the sum of the first $8$ terms is $3280$. What is the first term of the series?
This formula gives the sum ${S_n}$ of the first $ n$ terms in the geometric series where the first term is $ a$ and the common ratio is $C r$ : ${S_n}=\dfrac{ a(1-C r^{ n})}{1-C r}$ We are given the values for ${S_n}$, $ n$, and $C r$.Let's plug them in the formula and solve for $ a$. We are given that ${S_n=3280}$, ${n=8}$, and $C{r=3}$ : ${3280}=\dfrac{ a(1-C 3^{{8}})}{1-C 3}$ Solving the equation, we get that $a=1$. In conclusion, the first term of the series is $1$.